Provided are a method and apparatus for encoding and decoding images based on constrained offset compensation and a loop filter. The image decoding apparatus: receives, from an encoder, a first indicator indicating whether a sequence, a picture, a frame, a slice, a coding unit (CU), a prediction unit (PU), and/or a transform unit (TU) supports constrained offset compensation; receives, from the encoder, a second indicator indicating whether constrained sample adaptive offset (SAO) compensation or an adaptive loop filter (ALF) is applied; receives a parameter from the encoder; and applies the SAO compensation or the ALF to pixels of a restored image on the basis of the second indicator and the parameter.